1. Field of the Invention
The invention relates to a method and circuitry for developing a magnitude signal which represents the approximate magnitude of a control parameter vector for the control of a multi-phase electrical apparatus, such as a rotary field machine or a three-phase system.
2. Description of the Prior Art
In the control of rotary field machines and of threephase power supplies, the problem often arises of determining the magnitude of a vector (e.g. a voltage or current vector) which is defined by its coordinates. In the control of a rotary field machine, for example, a magnetizing current control produces the desired value for the magnetizing current, and an active current control the desired value for the active current, the two currents being phase-shifted by 90.degree., i.e., the respective vectors are perpendicular to one another. The rotary current machine is controlled with a current composed of the magnetizing current thus determined and of the active current, it being necessary to determine the magnitude of the current.
The seemingly most obvious method to use to determine the magnitude of a vector is the Pythagorean theorem. This method is, however, relatively complicated to implement with circuitry since it requires the use of two squaring components and a root evolving component. Moreover, analog squarers and root evolvers cause very high errors at small values.
Existing literature describes a circuit referred to as a "vector meter" for the formation of the magnitude of a vector. This circuit operates with a control loop which proceeds from a transformed formulation of the Pythagorean theorem. It requires two adders and a multiplier with division input. Analog dividers, however, are relatively complicated, and have limited accuracy at small values.
Another known possibility is the formation of the magnitude of a vector by approximation using the so-called "characteristic curve" method, which is employed in commercially available equipment. The characteristic used for this method is shown in FIG. 1. The x-coordinate V.sub.X of a vector V is plotted on the abscissa, and its magnitude .vertline. is plotted on the ordinate. The characteristic consists of a group of lines parallel to the ordinate with the y-coordinate of the vector V as parameter, and of the bisectors of the coordinate system. As long as the coordinates of the vector V lie in the zone of the group of straight lines, the y-component of the vector V is used in accordance with these lines as the magnitude .vertline. of the vector. For vector coordinates outside the group of lines, the magnitude .vertline. of the vector is determined from the x-coordinate by way of the respective bisector, that is, the x-coordinate is used as the magnitude. Since the group of lines of the characteristic comes into play when the y-coordinate of the vector V is greater than its x-coordinate, what the characteristic curve method amounts to in the last analysis is that the greater of the two coordinates of the vector V is chosen as the magnitude of the vector. The accuracy of this method, however, is very low. The maximum occurring error is about 30% and occurs when the two coordinates of the vector V are identical.